You're quite right to ask for a citation. Sadly I can't give you one as the TFL rail condition assessments aren't public. Instead I'll point out that Metronet and Tubelines spend billions trying to dig out of the backlog and failed
https://en.wikipedia.org/wiki/Tube_Lines
>no one wants to pay to replace them. So every night they need... replacing
Yeah, stupid right?
Imagine a signal is broken (and TFL still used vaccume tubes for its signal systems as recently as 2010). So you have to reduce speed on the line. So now the centra-pedal forces on the corner after the speed restriction aren't enough to counter the camber of that curve. So the wheels on ever train grind down the railhead. So now you have the replace the rail (or polish it etc) much sooner than expected.
Failing to replace one part forces you to replace another part. Replacing that part uses up the time/money you have so you can't now replace the first part.
Take the central line anywhere between Bank and Stratford some time. The screaming of the wheels isn't just deafening noise. It's the actual rail being turned into dust because no one has invested a weeks closure and money to fix the rest of the infrastructure. So instead every night someone has to go check it and make sure it hasn't cracked yet...